Householder reflectors: generation, blocking, application. More...

Functions/Subroutines
pure subroutine, public	la_slarf (side, m, n, v, incv, tau, c, ldc, work)
	SLARF: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix.

pure subroutine, public	la_dlarf (side, m, n, v, incv, tau, c, ldc, work)
	DLARF: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix.

pure subroutine, public	la_qlarf (side, m, n, v, incv, tau, c, ldc, work)
	QLARF: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix.

pure subroutine, public	la_slarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	SLARFB: applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right.

pure subroutine, public	la_dlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	DLARFB: applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right.

pure subroutine, public	la_qlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	QLARFB: applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right.

pure subroutine, public	la_slarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	SLARFT: forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V.

pure subroutine, public	la_dlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	DLARFT: forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V.

pure subroutine, public	la_qlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	QLARFT: forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VT If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VT * T * V.

pure subroutine, public	la_slarfx (side, m, n, v, tau, c, ldc, work)
	SLARFX: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_dlarfx (side, m, n, v, tau, c, ldc, work)
	DLARFX: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_qlarfx (side, m, n, v, tau, c, ldc, work)
	QLARFX: applies a real elementary reflector H to a real m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**T where tau is a real scalar and v is a real vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_slarfy (uplo, n, v, incv, tau, c, ldc, work)
	SLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n symmetric matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

pure subroutine, public	la_dlarfy (uplo, n, v, incv, tau, c, ldc, work)
	DLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n symmetric matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

pure subroutine, public	la_qlarfy (uplo, n, v, incv, tau, c, ldc, work)
	QLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n symmetric matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

pure subroutine, public	la_slarfg (n, alpha, x, incx, tau)
	SLARFG: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= tau <= 2.

pure subroutine, public	la_dlarfg (n, alpha, x, incx, tau)
	DLARFG: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= tau <= 2.

pure subroutine, public	la_qlarfg (n, alpha, x, incx, tau)
	QLARFG: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= tau <= 2.

subroutine, public	la_slarfgp (n, alpha, x, incx, tau)
	SLARFGP: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is non-negative, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix.

subroutine, public	la_dlarfgp (n, alpha, x, incx, tau)
	DLARFGP: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is non-negative, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix.

subroutine, public	la_qlarfgp (n, alpha, x, incx, tau)
	QLARFGP: generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H*T H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is non-negative, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix.

pure subroutine, public	la_clarf (side, m, n, v, incv, tau, c, ldc, work)
	CLARF: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH (the conjugate transpose of H), supply conjg(tau) instead tau.

pure subroutine, public	la_zlarf (side, m, n, v, incv, tau, c, ldc, work)
	ZLARF: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH, supply conjg(tau) instead tau.

pure subroutine, public	la_wlarf (side, m, n, v, incv, tau, c, ldc, work)
	WLARF: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * vH where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply HH, supply conjg(tau) instead tau.

pure subroutine, public	la_clarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	CLARFB: applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right.

pure subroutine, public	la_zlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	ZLARFB: applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right.

pure subroutine, public	la_wlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	WLARFB: applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right.

pure subroutine, public	la_clarfg (n, alpha, x, incx, tau)
	CLARFG: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .

pure subroutine, public	la_zlarfg (n, alpha, x, incx, tau)
	ZLARFG: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .

pure subroutine, public	la_wlarfg (n, alpha, x, incx, tau)
	WLARFG: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, with beta real, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 .

subroutine, public	la_clarfgp (n, alpha, x, incx, tau)
	CLARFGP: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is real and non-negative, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

subroutine, public	la_zlarfgp (n, alpha, x, incx, tau)
	ZLARFGP: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is real and non-negative, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

subroutine, public	la_wlarfgp (n, alpha, x, incx, tau)
	WLARFGP: generates a complex elementary reflector H of order n, such that H*H ( alpha ) = ( beta ), H*H H = I. ( x ) ( 0 ) where alpha and beta are scalars, beta is real and non-negative, and x is an (n-1)-element complex vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**H ) , ( v ) where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix.

pure subroutine, public	la_clarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	CLARFT: forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V.

pure subroutine, public	la_zlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	ZLARFT: forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V.

pure subroutine, public	la_wlarft (direct, storev, n, k, v, ldv, tau, t, ldt)
	WLARFT: forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector H(i) is stored in the i-th column of the array V, and H = I - V * T * VH If STOREV = 'R', the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and H = I - VH * T * V.

pure subroutine, public	la_clarfx (side, m, n, v, tau, c, ldc, work)
	CLARFX: applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_zlarfx (side, m, n, v, tau, c, ldc, work)
	ZLARFX: applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_wlarfx (side, m, n, v, tau, c, ldc, work)
	WLARFX: applies a complex elementary reflector H to a complex m by n matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix This version uses inline code if H has order < 11.

pure subroutine, public	la_clarfy (uplo, n, v, incv, tau, c, ldc, work)
	CLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n Hermitian matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

pure subroutine, public	la_zlarfy (uplo, n, v, incv, tau, c, ldc, work)
	ZLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n Hermitian matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

pure subroutine, public	la_wlarfy (uplo, n, v, incv, tau, c, ldc, work)
	WLARFY: applies an elementary reflector, or Householder matrix, H, to an n x n Hermitian matrix C, from both the left and the right. H is represented in the form H = I - tau * v * v' where tau is a scalar and v is a vector. If tau is zero, then H is taken to be the unit matrix.

Detailed Description

Householder reflectors: generation, blocking, application.

Function/Subroutine Documentation

◆ la_clarf()

pure subroutine, public la_lapack_householder_reflectors::la_clarf	(	character, intent(in)	side,
		integer(ilp), intent(in)	m,
		integer(ilp), intent(in)	n,
		complex(sp), dimension(*), intent(in)	v,
		integer(ilp), intent(in)	incv,
		complex(sp), intent(in)	tau,
		complex(sp), dimension(ldc,*), intent(inout)	c,
		integer(ilp), intent(in)	ldc,
		complex(sp), dimension(*), intent(out)	work )

CLARF: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form H = I - tau * v * v**H where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H**H (the conjugate transpose of H), supply conjg(tau) instead tau.